You need to finish obtaining all the rest of the AF (including the coffers) and then talk to
this guy who can reset the quests for 10k gil. It is not necessary to throw away the rest of your AF before talking to this guy, but if a piece you have is given as a reward for one of the quests (such as the weapon), you will be unable to complete the quest again until you throw your previous weapon away.
Edited, Jan 6th 2010 7:49am by Fynlar